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Diophantine Approximation on Linear Algebraic Groups : Transcendence Properties of the Exponential Function in Several Variables

Author: Michel Waldschmidt
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2000.
Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 326.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function e^z. A central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. This book includes proofs of the main basic results (theorems of Hermite-Lindemann, Gelfond-Schneider, 6 exponentials theorem), an introduction to  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Michel Waldschmidt
ISBN: 9783662115695 3662115697
OCLC Number: 851369860
Description: 1 online resource (xxiii, 636 pages).
Contents: Introduction and Historical Survey --
Part I. Linear Independence of Logarithms of Algebraic Numbers. Transcendence Proofs in One Variable. Heights of Algebraic Numbers. The Criterion of Schneider-Lang. Zero Estimate. Linear Independence of Logarithms of Algebraic Numbers --
Part II. Measures of Linear Independence. A First Measure with a Simple Proof. Zero Estimate (Continued), by Damien ROY. Refined Measure --
Part III. Multiplicities in Higher Dimension Multiplicity Estimates, by Damien ROY. Interpolation Determinants with One Derivative. On Baker's Method --
Part IV. The Linear Subgroup Theorem. Points Whose Coordinates are Logarithms of Algebraic Numbers. Lower Bounds for the Rank of Matrices --
Part V. Simultaneous Approximation of Values of the Exponential Function in Several Variables. A Quantitative Version of the Linear Subgroup Theorem. Applications to Diophantine Approximation. Algebraic Independence --
References.
Series Title: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 326.
Responsibility: by Michel Waldschmidt.

Abstract:

The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the  Read more...

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"The present book is very nice to read, and gives a comprehensive overview of one wide aspect of Diophantine approximation. It includes the main achievements of the last several years, and points out Read more...

 
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